Problem: The grades on a physics midterm at Covington are normally distributed with $\mu = 72$ and $\sigma = 2.0$. Stephanie earned a $74$ on the exam. Find the z-score for Stephanie's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Stephanie's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{74 - {72}}{{2.0}}} $ ${ z \approx 1.00}$ The z-score is $1.00$. In other words, Stephanie's score was $1.00$ standard deviation above the mean.